Viscoelastic deformations of a thick-walled cylinder under prolonged exposure to gravitational stresses

A method is presented for the calculation of the stress-deformed state of an infinitely long viscoelastic thick-walled cylinder, enclosed in an elastic casing and exposed to gravitational stress in equilibrium with a system of concentrated forces, applied to the casing. The problem is solved by analyzing the flat deformation of the annular region under the influence of mass forces and unknown reactions on the outer surface, and by determining the stress-deformed state of the casing ring exposed to distributed normal and tangential loads, and to a system of concentrated forces. The solutions are then compared on the basis of compatibility of the deformations and equality of the stresses. Integral transformations are used in the calculations and an example is cited.S. Ordzhonikidze Aviation Institute, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 846–853, September–October, 1972.     

Determination of mass entrainment of heat-insulating materials from the deformation of stressed casings

A method has been developed for the determination of mass entrainment and reinforcing layer boundaries of stressed casings subjected to erosion and thermal degradation. The method is based on the determination of the stresses acting on the casing and the measurement of casing deformation by means of tensometers (strain gages), installed on the external surface. Results obtained in the experimental verification of the method by model tests carried out on glass-plastic single and double-layer casings are presented.Deceased.P. I. Baranov Central Institute of Aeroengine Design, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 824–828, September–October, 1972.     

Nonsteady-state damage accumulation processes in composite flanges under cyclic loads

We consider two typical flanges: for a powerplant casing and for the casing of suspensions with a sound-absorbing duct. We model the behavior of flanges under the action of cyclic external loads based on solution of the nonlinear axisymmetric problem of elasticity theory. In order to take into account fatigue fracture of the layers of the structure, we use maximum stress criteria, a tensor damage function, the rule of linear summation of damage, and reduction schemes for the deformation characteristics of the layers, describing different fracture mechanisms. We indicate the possible nature of the development of fracture zones in composite flanges. We have established the spare load-bearing capacity of the flanges after fracture begins.Report presented at the Tenth International Conference on Mechanics of Composite Materials (Riga, April 20–23, 1998).Perm State Technical University, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 5, pp. 636–643, September–October, 1997.     

Verification of the hypothesis of the existence of a potential with reference to teflon

In establishing the rheological relations describing the behavior of materials during deformation it is often very useful to employ a potential function. The hypothesis of the existence of a potential is verified in relation to the deformation of teflon in a complex state of stress.Scientific-Research Institute of Mathematics and Mechanics, Leningrad Zhdanov State University. Translated from Mekhanika Polimerov, No. 3, pp. 565–567, May–June, 1969.     

Flexure of transversely isotropic plates with a low resistance to transverse deformation

This study is concerned with the stress field around holes in plates of a transversely isotropic material, such as a reinforced plastic, with a low resistance to transverse, normal, and tangential deformation. The problem is solved on the basis of the general theory according to I. N. Vekua. It is shown that in the case of a strongly anisotropic material disregarding the transverse deformation will lead to a large error in the determination of the stress field.Institute of Metallurgy, Dnepropetrovsk. Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 1, pp. 89–92, January–February, 1974.     

The selection of optimum parameters for a cylindrical fiberglass plastic casing under axial compression

A modern mathematical optimization method — the random search method — is applied to nonlinear programming with the aim to select the parameters of an axially compressed fiberglass plastic cylindrical casing which minimize its weight and, at the same time, satisfy the strength and stability requirements.Dnepropetrovsk Engineering Constructions Institute. Translated from Mekhanika Polimerov, No. 5, pp. 945–946, September–October, 1972.     

On the deformation of an extended viscoelastic rod subject to finite deformations

The deformation of a polymer material subjected to tensile strain is considered with due allowance for physically linear creep at finite deformations. The deformation process is only stable in time up to a certain value of the load; under heavier loads the deformation is unstable. An expression is derived for the critical time.Institute of the Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 6, pp. 1130–1133, November–December, 1972.     

Deformation of elastic polyurethanes with a bimodal cellular structure

This article examines the cellular structure and mechanical properties of elastic foamed polyurethanes with a bimodal cellular structure (BFPUs). It is shown that the sizes of the oval cells (3–12 mm) in the elastic foamed polyurethenes that are studied are a tenth of an order greater than the sizes of the polyhedral cells (0.1–0.6 mm). Conversely, for rigid foamed polyurethanes, the polyhedral cells are more than a tenth of an order larger than the oval cells (microcells). The equations of the compression curve of BFFUs are found, and it is established that the deformation of BFPUs is determined by the deformation function of the cellular structure and the viscoelastic properties of the polymer matrix. The deformation functions of the cellular structure and the relaxation properties of BFPUs are determined. It is shown that choosing BFPUs with a cellular structure improves the comfort properties of the foamed material: the softness coefficient increased by 8–19% in the investigated case, while the support coefficient increased by 15–35%.Paper presented at the IX International Conference on the Mechanics of Composite Materials (Riga, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 32, No. 3, pp. 330–339, May–June, 1996.     

Finite-element analysis of the stability of a stiffening rib of complex shape

The finite-element method is applied to analyze local loss of stability of a complex stiffening rib. The elastic and geometrical stiffness matrices are obtained. The critical stresses where instability sets in are determined by solving an eigenvalue problem.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 66, pp. 60–70, 1988.     

A matrix algorithm for computing the coefficients of the transformation of waves on a reinforcing rib

In the work a matrix algorithm is proposed for computing the transformation coefficients (the coefficients of reflection, transmission, and transformation into waves of other types) for any vector fields and any angles of incidence. The method is illustrated by computing the transformation coefficients of vibrational waves on a rectilinear reinforcing rib reinforcing a plate and an annular rib reinforcing a thin, cylindrical shell.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 89, pp. 134–151, 1979.     

Effect of liquid media on the deformation of the surface layers of a polymer-metal pair in sliding friction

The relation between the high-elastic component of polyurethane deformation and the deformation of the surface layers of metals has been investigated for sliding friction in various media. The surface layers of polymer and metal are plastically deformed. There is a certain correlation between the coefficient of friction and the amount of deformation.Kiev Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, No. 1, pp. 147–149, January–February, 1970.     

Repairing force for deformed casing shaping with spinning casing swage and damage behaviour of cement sheath

In oil and gas fields, the repairing force (bit weight) is generally determined by experience when the deformed casing is repaired using the spinning casing swage. However, unreasonable repairing force easily damages the cement sheath around the deformed casing and causes pipe sticking, which results in failure of the wellbore integrity. Hence, based on the Hertz contact theory, the present study established a mechanical model to calculate the repairing force required to repair the deformed casing without a cement sheath by spinning casing swage, and the reshaping force was determined by combining the structural features of the spinning casing swage with the method of mechanics and kinetics analysis regarding axial loading and circumferential deformation of the deformed casing. Finally, a mechanical model was presented that could calculate the repairing force of the deformation casing with cement sheath using the inversion method. Repairing experiments involving three types of deformed casings (casing without cement sheath, casing with undamaged cement sheath and casing with damaged cement sheath) were performed, from which the accuracy and reliability of the mechanical model was validated. The damage behaviour of the cement sheath after casing repair was investigated based on the experimental results and the damage mechanism was analysed based on Saint-Venant's deformation compatibility principle. Analysis results showed that three types of damage, including micro-annulus, transverse fracture and longitudinal fracture, were caused by high contact pressure between the steel ball on the spinning casing swage and the internal wall of the deformed casing and pressure fluctuation during repairing. The research results provide important guidance and decision making for practical repairing measures.     

Variation of the elasticoviscous characteristics of a heavily filled rubber after periodic shear deformation

The results of an investigation of the recovery of the elasticoviscous characteristics after thixotropic reduction by periodic deformation in the nonlinear zone are reported. The rate of recovery of the mechanical properties depends on the deformation frequency and the previous history of dynamic deformation is shown to affect the dependence of the elasticoviscous characteristics on the shear rate gradient. The effects of stationary and dynamic deformation regimes on the relaxation spectrum of the material are compared.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 528–533, May–June, 1969.     

Dynamic deformation of a stationary rubber flow

The effect of dynamic deformation on the stationary flow of a rubber composition has been experimentally investigated for comparable values of the stationary and dynamic strain rates. The dependence of the effective viscosity on the stationary shear rate is not equivalent to its dependence on the periodic shear rate amplitude. An expression is given for calculating the effective viscosity in the case of combined stationary and dynamic shear deformation. The effectiveness of the dynamic deformation, estimated in terms of the effective viscosity, depends on whether it is superimposed on the stationary flow at constant stationary shear rate or at constant stress. It is proposed to estimate the effectiveness of dynamic deformation of a stationary non-Newtonian flow in terms of the change in the power of the stationary forces. When the effective viscosity is reduced by dynamic deformation of the stationary flow, the power of the stationary forces increases at constant shear stress and falls at constant stationary shear rate.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 489–496, May–June, 1971.     

Large deflections and rigidity of a long cylindrical orthotropic glass-plastic panel subjected to intermittent-uniform loads

Large deflections and the stability of a long slanting orthotropic cylindrical panel, subjected to an external pressure uniformly distributed over a section of the panel width, are discussed. Relationships are used, taking into account lateral-shift deformation and normal stress _z. A closed-loop solution is obtained by means of generalized functions. A numerical evaluation has been made to assess the error of Kirchhoff's hypothesis. Similar solutions, taking into account the lateral-shift deformation are presented in [4, 5] for cases involving continuous uniform pressure and local linear loads.Kazan Physicotechnic Institute, Academy of Sciences of the USSR. Translated from Mekhanika Polimerov, No. 5, pp. 829–837, September–October, 1972.     

Deformation and sliding friction of polyurethane in the presence of a lubricant

The relation between coefficient of friction and elastic and high-elastic strains is investigated with reference to polyurethane subjected to friction in various liquid media. It is shown that a definite relationship between these parameters does exist. The effect of various liquids on the elastic and high-elastic deformation of polyurethane is studied.Kiev Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, Vol. 5, No. 2. pp. 357–359, March–April, 1969.     

Deformation of rigidly clamped specimens of acrylic plastics subjected to one-sided cyclic heating

The effect of one-sided rapid cyclic heating on the deformation of rigidly clamped specimens of acrylic plastics has been investigated. It is shown that as the temperature drop increases, so does the bending deformation (concave toward the heated surface) of the unclamped specimens; the greatest temperature change during thermal cycling is concentrated in an active surface layer not more than 1.6 mm thick and is accompanied by the development of tensile stresses in that layer. The characteristics of the reversibility of the deformation upon subsequent annealing are examined.Riga Institute of Civil Aviation Engineers. Translated from Mekhanika Polimerov, No. 1, pp. 85–90, January–February, 1976.     

Deformation of a glass-reinforced plastic cylindrical shell encased in a thick-walled elastic cylinder

A solution is given for the axisymmetric problem of the deformation of an orthotropic glass-reinforced plastic shell of finite length encased in a soft transversely isotropic cylinder under internal pressure.Moscow Institute of Heat Engineering. Translated from Mekhanika Polimerov, No. 1, pp. 164–168, January–February, 1973.     

Deformation of a flexible current-carrying plate in a constant magnetic field

A solution procedure is proposed for the deformation of current-carrying annular plates with nonlinear geometry in a constant magnetic field. We assume that the deformation of the plate by the time-dependent Lorentz force is a slow process and the inertial terms can be ignored. The problem is solved numerically by quasilinearization and discrete orthogonalization methods.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 65, pp. 67–70, 1988.     

Diffraction of sound on a spherical shell with a ring-shaped rib

We obtain a closed-form solution of the axisymmetric problem of the echo-signal from a thin spherical shell containing an elastic ring. We analyze the influence of the reinforcing rib on the frequency dependence of the scattering amplitude in the axial direction and also on the directional characteristics in regimes of potential and resonance scattering.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 143–146.